A point is called integral if both and are integers. How many points on the graph of are integral points?Source: NCTM Mathematics Teacher, November 2006

SOLUTION
Divide by ,
Divide by
Divide by , no solution, duplicate solution
Divide by , no solution
Divide by , no solution, duplicate solution , duplicate solution
Divide by , no solution, no solution, no solution
Divide by , no solution, no solution, no solution, duplicate solution
We found five solutions . We need an algebraic way to find all the solutions.
For to be an integer must divide . It’s positive divisors yield the five previous solutions. The negative divisors yield four more solutions, namely . One solution is discarded because and . Nine points on the graph are integral points.